z=(x−a)2+(y−b)2Differentiating partially with respect to x and y, we get
∂x∂z=2(x−a)∂y∂z=2(y−b)Squaring and adding these equations, we have
(∂x∂z)2+(∂y∂z)2=(2(x−a))2+(2(y−b))2(∂x∂z)2+(∂y∂z)2=4((x−a)2+(y−b)2)Since (x−a)2+(y−b)2=z, we get
(∂x∂z)2+(∂y∂z)2=4z
Comments
Leave a comment